Investing is an activity which is often made unnecessarily complex. Many investment professionals, such as financial advisers and portfolio managers, too often contribute to their client’s confusion by failing to adequately explain basic financial concepts. In this guide, we explain five of the most important concepts which investors should know before making financial decisions. And while one concept, active vs. passive investing, refers to financial assets such as stocks and bonds, the other four concepts apply to investments in other asset types including real estate and private businesses.

Money has time value in the sense that a monetary sum today is worth more than the same sum in the future. This is not only due to inflation (the decline in money’s purchasing power over time) but also because of (a) the uncertainty that the future sum will be realized and (b) the foregone interest which could have been earned over that period.

An investor can determine the worth of a future sum through a mechanism known as discounting. The value derived from discounting a future sum is the present value. The formula for calculating present value is:
PV = FV / (1 + r)n where FV is the future sum, r is the investor’s desired rate of return per period, and n is the number of periods.
Conversely, the investor can calculate the future value of a present sum through a mechanism known as compounding. Compounding refers to the actual rate of growth of a sum over a period. The formula for calculating future value is:
FV = PV(1 + r)n
where PV is the current sum, r is the investor’s desired rate of return per period, and n is the number of periods.

Conversely, the investor can calculate the future value of a present sum through a mechanism known as compounding. Compounding refers to the actual rate of growth of a sum over a period. The formula for calculating future value is:

FV = PV(1 + r)n
where PV is the current sum, r is the investor’s desired rate of return per period, and n is the number of periods.

Because an investor’s monetary resources are limited in quantity, the investor must choose among competing investments. To pursue an investment, the investor must forgo other investments with similar risks. The return which is foregone when the investor pursues an investment over alternatives is the investor’s opportunity cost. This concept is the basis for an investor’s desired return (required return) on a specific investment. Suppose, for example, that an investor is presented with a bond yielding 5%. The investor determines that bonds with similar risks are available with 7% yields. Despite the positive return on the 5% bond, the investor would suffer an economic loss of 2% in that the investor had foregone a 7% yield on a similar instrument. This is an important point: an investor will only increase her economic wealth when an investment offers a return in excess of the investor’s required return.

All investors can earn, with minimal risk, the rate on short-term government securities – a rate often referred to as the risk-free rate. An investor’s required rate of return on a specific investment should thus be a function of (a) the risk-free rate and (b) an appropriate risk premium. While the rate on short-term government securities is generally used as the risk-free rate, the asset’s risk premium is more subjective. However, the asset type’s average historical returns minus the rate on government bonds is often used as the asset’s risk premium. For example, stock investors may use the average returns on the S&P 500 stock index minus the rate on the 10-year government note as the appropriate risk premium for analyzing a stock.

Investors in common stocks must decide if they should actively select stocks (or hire someone to do it for them) or invest in a fund which mimics a stock index, such as the S&P 500. Since an investor can match the returns of the broadly-diversified S&P 500, the returns on this index represent the stock investor’s opportunity cost.

Active stock selection represents a stock portfolio based on fundamental or technical analysis.

Fundamental analysis involves analyzing the company’s financial statements and business prospects to determine if the stock offers a favorable risk-return tradeoff. Technical analysis relies on reading stock-price charts to forecast the future movements of stock prices. Regardless of the method of stock selection, most individual investors have neither the time nor the training to select stocks on their own. However, investors can hire professional portfolio managers to select stocks for them. The most common form of professional management is through mutual funds, which are commingled pools of professionally managed capital. High net-worth investors may also invest in hedge funds, which are private investment partnerships which often employ more exotic investment strategies. Finally, some firms offer professional portfolio management through separately managed accounts in which stocks are purchased directly for the client’s individual account.

Financial markets are highly competitive, and many professional investment mangers fail to earn returns in excess of returns on passive instruments. If an investor decides to seek out the services of a professional manager, the investor should ask the manager what his or her investment “edge” is, i.e., the reason why the manager believes he or she can generate excess returns. If the manager cannot convincingly articulate his or her edge, the investor should consider a passive instrument such as an index fund.

For those seeking to learn more about active and passive investing, we have a white paper, Performance Constraints in Investment Management, available for download here.

In its simplest form, diversification refers to an investor’s spreading of risk by purchasing assets whose returns behave differently in different economic conditions. Investors should diversify among asset classes (stocks, bonds, real estate, etc.) and among individual securities within each asset class. Diversification is one approach to reducing an investor’s risk.

Diversifying among common stocks can help reduce firm-specific risk (also called nonsystematic risk). This is the risk that the value of a company’s stock can become impaired due to circumstances unique to the company. One mathematical approach to diversification is modern portfolio theory (MPT). MPT employs mathematical techniques to optimize the relationship between a portfolio’s risk and its expected return. MPT uses the asset’s past price volatility as a quantifiable measure of risk, with volatility being measured as period-over-period deviations from average returns (the specific metrics are variance and standard deviation). By selecting securities whose past returns are uncorrelated (between a measure of 1 for perfect correlation and -1 for perfect negative correlation), investors can construct an “optimum” portfolio, i.e., a portfolio offering the lowest volatility for a given level of expected return.

While we agree with the conceptual framework behind MPT, we are skeptical of its use for several reasons. First, MPT deemphasizes the role of fundamental analysis and stock valuation. Under MPT, a stock should be purchased for its diversification benefits to a portfolio, rather than because the stock is undervalued. Second, we believe that price-volatility is a poor measure of investment risk. In our view, investment risk is the potential for a permanent impairment in an asset’s value. Too many factors can contribute to an investor’s loss to be captured in a single variable. Third, for the MPT practitioner to rely on past returns, she must determine both (a) the interval of those returns (weekly, quarterly, etc.) and (b) the length of time over which the returns are observed. Changing the intervals and length of the observations can significantly alter the MPT mathematics. Finally, MPT assumes that past statistical relationships will persist in the future. This can be a flawed assumption when, for example, a company is in a different business than they were in in the past.

Despite our skepticism towards MPT, investors should diversify among asset classes and individual securities. When constructing portfolios, investors should think about how the asset will respond to different economic conditions.

Value investing is a method of purchasing an asset when the price of that asset is significantly below the investor’s appraisal of fundamental value. This difference between value and price is what Benjamin Graham, the father of fundamental stock analysis, referred to as the margin of safety.

A reliable appraisal of fundamental value is key to the margin of safety concept. Valuation is generally derived by either discounting the asset’s expected future cash flows, known as discounted cash flow (DCF) analysis, or by observing prices of comparable assets. In our opinion, DCF is the more theoretically sound method of asset valuation. In a previous section, we presented the formula for calculating the present value of a single sum. For a perpetual cash flow stream used in the basic DCF model, the investor uses the following formula:

Value = CF / (r – g)
where CF is the asset’s current cash flow normalized to eliminate nonrecurring items, r is the investor’s required return, and g is the perpetual rate of growth of the cash flows.

The above formula gives the investor a value against which the asset’s price can be compared. And while the components can be subjective, the investor can enhance the usefulness of the valuation by using conservative assumptions. In addition, by pairing the margin of safety concept with the concept of diversification, the investor can create a very sound portfolio.

While we have presented what we believe to be the five most important investment concepts, we must recognize that these are not the only important investment concepts. Education in this field, as in all fields, is best thought of as a journey. We hope this paper represents a first step.


Defusco, Richard A., Dennis W. McLeavey,

Jerald E. Pinto, David E. Runkle.

Quantitative Investment Analysis, 2nd ed. Hoboken: Wiley, 2007.

Graham, Benjamin. The Intelligent Investor, revised ed. New York: Harper Business,


Reilly, Frank K, and Edgard A. Norton.

Investments 6th ed. Mason: South-Western, 2003.